Factor the following expression: $7$ $x^2+$ $5$ $x$ $-2$
Answer: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(7)}{(-2)} &=& -14 \\ {a} + {b} &=& & & {5} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-14$ and add them together. Remember, since $-14$ is negative, one of the factors must be negative. The factors that add up to ${5}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-2}$ and ${b}$ is ${7}$ $ \begin{eqnarray} {ab} &=& ({-2})({7}) &=& -14 \\ {a} + {b} &=& {-2} + {7} &=& 5 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {7}x^2 {-2}x +{7}x {-2} $ Group the terms so that there is a common factor in each group: $ ({7}x^2 {-2}x) + ({7}x {-2}) $ Factor out the common factors: $ x(7x - 2) + 1(7x - 2) $ Notice how $(7x - 2)$ has become a common factor. Factor this out to find the answer. $(7x - 2)(x + 1)$